Finally, we consider an  kNN method for downsampling, inspired by [1]}, where we only use the \(k\)  closest data points to the new data \(\tilde{y}^n_k\)  in the constraints described in Remark REF . This strategy is a form of lazy learning with no required preprocessing nor extra memory. Since only \(k\)  points are taken into consideration for each \(\tilde{y}^n_k\) , computational time and number of constraints for the resulting algorithm can both decrease. However, the complexity of kNN algorithm, \(\mathcal {O}(nd+kn)\) , indicates that it may be time-consuming to formulate the model invalidation problem for a large data set  with kNN-based downsampling.
